There are several methods that are traditionally used to measure force. These include resistive, foil, semiconductor, wire and thin film strain gauges as well as hydraulic and pneumatic load cells. Of these, most are indirect—i.e. the sensor itself is not in contact with the force. Rather, the sensing element is placed remote from the force, but is positioned in such a way that it undergoes change in response to the force. For example, the resistive strain gauge load cell has a resistance in the cell that changes with deflection of a mechanical component. As is common to all indirect techniques, placement of the indirect sensor is critical. In contrast to the indirect method, a sensor that is capable of measuring force directly has significant benefits. These include placement of the sensing device anywhere the force is transmitted.
The use of piezoelectric materials to measure force has several potential advantages. They are relatively inexpensive compared to load cells, they measure force directly, and are they are easy to form into a wide variety of shapes and sizes. Sensors for large panels the size of a basketball backboard or a small circular ring are readily achieved. They are extremely robust and can measure over a very large range with precise linear response. Finally, these sensors have excellent high frequency responses due to their high natural frequencies.
In general, piezoelectric materials have not been applied for applications in which force is applied for periods of time of many seconds/minutes. This is in large part due to required integration that is necessary to convert voltage from the sensor to a value of force. Analog based circuits constructed for the integration have tended to drift-leading to large sensor errors.
In a piezoelectric material, as a first approximation, the charge produced is linearly proportional to the applied stress or force:Q∝Force  (1)
The most prevalently used materials that exhibit strong piezoelectric properties are quartz crystal, tourmaline, gallium orthophosphate, certain ferroelectric ceramics such as lead-zirconite-titanate (PZT), and special polymer films such as polyvinylidene fluoride (PVDF). An actuator makes better use of PZT due to its larger strain constant. On the other hand, PVDF film is better used in sensor applications with its relatively larger stress constant. PVDF, or piezoelectric film, is a thin plastic polymer. It can be purchased in sheets and custom cut to the desired shape and size.
A few circuit models are provided to set forth the operation and use of piezoelectric devices. FIG. 1 is a representation of a piezoelectric film material in which an applied force is shown that compresses the thickness portion of the device. As a result of polarization, positive and negative charges develop at the opposing conductor surfaces respectively.
The equivalent circuit in FIG. 2 shows a charge source that is defined to be proportional to the applied force. The capacitor is inherent to the device, functions as a storage device since it is the location of the electric field, and will present a voltage equal to charge divided by the capacitance. Electrically speaking, a piezoelectric sensor is a capacitor with the piezoelectric element acting as a dielectric. Because the dielectric exhibits a piezoelectric effect, a piezoelectric sensor can be considered as an active capacitor that charges itself when mechanically loaded. The resistance is due to the nonzero conductivity of the dielectric. Therefore, the voltage present across the terminals of a piezoelectric device will always decay to zero. This is one of the few reasons that true dc measurement of force is not possible using piezoelectric sensors.
A charge source is not a typical circuit element. Therefore, it is more convenient to use a standard voltage or current source. Since the definition of current is the time rate flow of charge, one can simply substitute the charge source for a dependant current source. FIG. 3 shows this modification. The short circuit current is proportional to the time derivative of charge as in Equation (2).
                              I          sc                ∝                              ⅆ                          ⅆ              t                                ⁢                      Q            ⁡                          (              t              )                                                          (        2        )            
From Equation (1), the current and applied force can be related as
                              I          sc                ∝                              ⅆ                          ⅆ              t                                ⁢          Force                                    (        3        )            
The output of any piezoelectric material due to stress or strain is electric charge. Charge can be a difficult quantity to measure and conceptualize compared to voltage or current. Another difficulty is that the quantity of charge realized is in the 10−12 coulomb (C) range.
Since charge produced by a piezoelectric sensor is relatively small, direct connection to a volt meter, analog-to-digital converter or even an oscilloscope is not practical. The combined resistance of the sensor, cabling, and measurement device loads the sensor and causes an amplitude loss and phase shift.
An electrometer amplifier is a very sensitive voltage amplifier specifically designed to make very high impedance measurements. FIG. 4 shows a piezoelectric sensor connected to an electrometer amplifier using a coaxial cable. For use with piezoelectric sensors, a gain of 1 is common. The amplifier allows a voltage to increase across the sensor as opposed to subsequent amplifiers. Its output is proportional to the sensor voltage, and is capable of driving lower impedance loads. Thus, the amplifier is an impedance buffer.
A range capacitor, Cr, is usually placed in parallel with the sensor to obtain different sensitivities or measuring ranges for the system. This is due to the fact that the voltage developed across the total capacitance of the input is related to the ratio of charge divided by capacitance. Increasing the range capacitor lowers the input voltage for a given applied force to the sensor. This is done to limit the voltage present at the input terminals of the amplifier so that the amplifier operates in its linear region.
The reset switch that is also in parallel with the sensor is used to discharge or “reset” the output to zero. In practice, a small valued resistor is usually placed in series with the switch to prevent dead shorting the capacitor. This switch allows the initial output voltage to be zeroed independent of the current applied load. The amplifier can be reset with half the rated force on the sensor. Then small perturbations on top of this would respond just as linearly as if there were no load on the sensor.
Electrometer amplifiers are prone to several disadvantages. The sensitivity of the output is not inversely proportional to the range capacitor. This is due to the fact that the sensor and cable capacitance also contribute to the total capacitance. Therefore, doubling the value of the range capacitor does not cut the sensitivity in half. It is also bothersome that any voltage developed across the sensor will decay due to leakage resistance. For the output to not drop appreciably over long time periods, equivalent leakage resistances in the hundreds of TΩ are required. The leakage resistance of the cable can also change with age and use. It is therefore not an ideal solution for quasi-static measurements.
A charge amplifier makes a significant improvement in charge measurement. The charge amplifier has had a significant impact on the practicality of using piezoelectric sensors. The term charge amplifier is actually a misnomer as the charge developed by the sensor is not amplified. Instead, the charge produced is converted to a proportional voltage. Here and elsewhere however, charge amplifier is the commonly accepted name.
An ideal charge amplifier is shown in FIG. 5. An operational amplifier is configured as an integrator using a negative capacitive feedback. Assuming that the op amp is ideal, the voltage potential from the inverting to non-inverting input is zero. This implies that the voltage across the sensor is zero. Using Kirchhoff's current law at the inverting inputIpiezo+IC+Iinput=0  (4)Ideally, the input current of the op amp is zero. The current developed from the sensor will be the short circuit current determined in Equation (2). The capacitor current is then
                                          I            C                    ⁡                      (            t            )                          =                  -                                    ⅆ                              Q                ⁡                                  (                  t                  )                                                                    ⅆ              t                                                          (        5        )            Since the inverting input is virtually referenced to ground, the output of the circuit is equal and opposite the voltage present on the feedback capacitor. The output voltage is therefore
                                          V            out                    ⁡                      (            t            )                          =                                            -                              1                                  C                  r                                                      ⁢                          ∫                                                                    I                    C                                    ⁡                                      (                    t                    )                                                  ⁢                                  ⅆ                  t                                                              =                                    -                                                Q                  ⁡                                      (                    t                    )                                                                    C                  r                                                      +                          V                              I                .                C                .                                                                        (        6        )            Thus, the charge amplifier integrates the short circuit current developed by the sensor.
The second term in Equation (6) represents the initial condition or voltage present on the feedback capacitor. Similar to the electrometer, this value can be zeroed by closing a reset switch that is in parallel to the range capacitor. In contrast to the electrometer, the capacitor is part of the feedback and is not in parallel with the sensor.
Charge amplifiers have greatly increased the number of practical applications of piezoelectric sensors, particularly for measuring quasi-static forces. However, despite numerous advantages, charge amplifiers create a host of implementation issues. The most significant is the problem of drift.
Drift in charge amplifiers is defined as the tendency of the output voltage to slowly increase or decrease over time. A drifting output is not a function of the applied stress and is therefore undesirable. Using op amps, drift will continue in either direction until the output is saturated. Drift is a problem for any integrating system exposed to non-zero biased inputs. Presently, there are two methods used to circumvent drift in analog charge amplifiers: a reset switch or a time constant resistor.
The reset switch depicted in FIG. 5 can be closed until the applied force is known to be changing. This stops all integration due to drift, but also forces the output to zero. Another disadvantage to this approach is “operation jump.” After the switch is released, it is common for the output to jump or shift in value. Two sources can be blamed for the jump: the operational amplifier's inherent noise and any residual charge on the reset switch.
Therefore, there is a need for a system and method to enable more accurate average force measurement using a piezoelectric material.